Update Dec 2, 2011: Lee Morrison at Urban Combatives recently expanded on the idea of the Peek-A-Boo as a distinct tactic by combining it with some other more or less instinctive positions commonly used by well known instructors such as Tony Blauer's "SPEAR" and calling the positions collectively "default positions." Interesting idea and worth reading I think. I was leading up to something like this in the article here but never got around to following up, but I think Lee did a better job than the one I would have done.
The Peek-A-Boo as a Distinct Tactic
It is notable in that the best known Asian traditions mostly use tactics where you stand upright, hands down or outstretched, grabbing or trapping limbs and striking while moving into close range. In Western boxing, the hands are usually held in front of the chin and beside the jaw.
The "peek-a-boo" tactic differs in that the fighter places both hands on his head (or sometimes at brow level), blocking with his forearms and elbows, and then in some variations may use this defense as part of a guarded rush to force the opponent back and engage them at close range. The position may appear momentarily in some form in boxing and Asian martial arts while covering up, but it becomes a distinct "Peek-A-Boo Tactic" when it is heavily relied on for its own unique characteristics.
A number of styles seem to treat this tactic as if they originated it, but it is likely that it was developed in parallel because relies on some of our gross defensive instincts, such as hunching over and pulling our body away from attack and raising our shoulders and arms to cover our face. That's probably why it is so highly favored in "reality-based" martial arts training, it requires little formal training and little fine motor skill to use effectively under a wide range of conditions.
The Peek-A-Boo in Boxing
The first place I know of that this tactic was used with dramatic effectiveness was in boxing. The legendary Cus D'Amato trained two world champion boxers in it: Floyd Patterson and Mike Tyson. Both used it to great effect at times. Wikipedia has a useful description of the Peek-A-Boo tactic as used in boxing:
"Peek a boo boxing utilizes relaxed hands with the forearms in front of the face and the fist at nose-eye level, as opposed to the orthodox style where the hands are at chin level with the left hand slightly in front of the chin and the right hand next to the chin. Other unique features includes side to side head movements, bobbing, weaving and blind siding your opponent. The number system e.g. 3-2-3-Body-head-body or 3-3-2 Body-Body-head is drilled with the stationary dummy and on the bag until the fighter is able to punch by rapid combinations with what Cus calls "bad intentions". The style allows swift neck movements as well quick duckings and the bad returning damage, usually by rising uppercuts or even rising hooks."
The Peek-A-Boo in Martial Arts
The use of the tactic in martial arts follows this pattern as well, but expands on it. The hands are kept high (often actually being placed on the top of the head when defending), moving from side to side continually but also moving the hands continually to faciliate quick blocking reactions. Martial artists are concerned with attacks from a wider range of angles than boxers and allows a wider range of counter-attacks, so the Peek-A-Boo in martial arts has to make more use of active blocking to cut off the angles and counter-attack.
You find this tactic featured in some martial arts of African origin and it is featured prominently in "Jailhouse Rock," an art of recent origin which a number of sources have testified to finding in modern prisons. The link to Jailhouse Rock is probably not coincidental. One version of the story of Floyd Patterson says that it was Patterson's use of the tactic he learned in Coxsacki prison that led to Cus D'Amato developing it for boxing. This story can only be partially true at best, however, since D'Amato had already taught a similar kind of defense to fighters before working with Patterson. In any case, whether boxing learned the tactic from prison, or prison from boxing, the tactic appears in similar forms in boxing and in penal fighting. There are many ways that the two could influence each other back and forth because of the unfortunate fact that many professional boxers have done prison time.
In this scan from John S. Soet's book Martial Arts Around the World, the aggressive use of elbows from a loose Peek-A-Boo defense is shown as an illustration of Jailhouse Rock.
The tactic is found in a number of other modern systems as well. Defensive Tactics instructor Steve Tarani teaches a stationary version of the tactic for fast emergency defense and calls it the QuickShield (a name he trademarked). It is found in informal versions in self-defense arts such as Brazilian Jiu-Jitsu, where it is used very briefly as a temporary defense and as a way to get into close range more safely rather than as a formal defensive system. I don't know if they use it in the Israeli arts, but I'd be very surprised if it didn't appear there somewhere. The heavily Indonesian flavored Jeet Kune Do of Dan Inosanto makes good use of this tactic and similar ones. The tactic has recently been featured in the fighting scenes of several movies. There is an interesting variation sometimes seen where one hand takes on the Peek-A-Boo posture on the head and the other hand braces against that elbow.
Mel Gibson is shown below doing a variation of the Peek-A-Boo.
More formally, the tactic is featured very prominently in several fighting systems as well. It is particularly apparent in the "Crazy Monkey Defense," and the Keysi Fighting Method. In the Keysi system, a particularly versatile form of the Peek-A-Boo is called the Pensador or "Thinking Man" and is used in a very aggressive way very similar to the boxing application.
The folks at Crazy Monkey Defense (Rodney King and friends) say that they invented the Peek-A-Boo tactic from watching monkeys while on safari. They use in primarily in a defensive boxing context, by keeping hands constantly in motion so as to use forearms for rapid blocking without giving up the defensive shield. Their use of Peek-A-Boo differs slightly from D'Amato's mainly in that they are initially teaching it purely as a defensive system and use blocking motions with the arms (as shown in the jab defense example below) rather than bobbing and weaving. This probably makes the defensive shield easier for beginners to utilize effectively, while at least temporarily giving up on the potentially aggressive use of the tactic.
Keysi Fighting Method
The Keysi Fighting Method was created by Justo Dieguez and Andy Norman in the 1950's and they say it originated in the "Spanish Gypsy streets." It heavily emphasizes a form of the Peek-A-Boo as a unique sort of aggressive defense in order to get into close range and set up close range strikes. In the Keysi system, the shield position is maintained continually and used to set up strikes and guarded rushes at close range. The Keysi method demonstrates the unique versatility of the Peek-A-Boo for both offense and defense when used in a more general martial arts application. The founders of the art also train in Jeet Kune Do with Dan Inosanto, which probably helps explain why it shares a lot of similarity in places with Kali, Silat, and other Indonesian martial arts. The Keysi method has received a lot of attention due to being featured in several popular Hollywood films such as Batman Begins, The Dark Knight, and MI-3.
The central concept in the Keysi method is the Pendador ("Thinking Man") which is the name they give the mobile, aggressive use of their particular version of the Peek-A-Boo position, with hands overlapping on the head. Many other concepts involve the use of that position to set up close range attacks.